Irrational Number and transcendental number

Question

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".Statement-1 :r is equivalent to either q or p.Statement-2 :r is equivalent to ~(p &harr; ~q).

ronit bhatiya · Accepted Answer

p : x is an irrational numberq : y is a transcendental numberr : x is a rational number iff y is a transcendental number=> r : ~ p &harr; qs1 : q or ps2 : ~ (p&harr;~q)pq~p~qr:~p&harr;qs1:q or pp&harr;~qs2:~(p&harr;~q)TTFFFTFTTFFTTTTFFTTFTTTFFFTTFFFTBased upon above charts1 and r are not equivalents2 and r are not equivalent

p	q	~p	~q	r:~p↔q	s₁:q or p	p↔~q	s₂:~(p↔~q)
T	T	F	F	F	T	F	T
T	F	F	T	T	T	T	F
F	T	T	F	T	T	T	F
F	F	T	T	F	F	F	T

Algebra> Irrational Number and transcendental numb...

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".Statement-1 :r is equivalent to either q or p.Statement-2 :r is equivalent to ~(p ↔ ~q).

swati shrivastav , 16 Years ago

ronit bhatiya

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Algebra> Irrational Number and transcendental numb...

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".Statement-1 :r is equivalent to either q or p.Statement-2 :r is equivalent to ~(p ↔ ~q).

swati shrivastav , 16 Years ago

ronit bhatiya

Provide a better Answer & Earn Cool Goodies

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Ask a Doubt

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